Riesz transforms for laguerre expansions

Abstract

We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any α > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted V inequalities, 1 < p -1, we make use of transplantation and some weighted inequalities we obtain in the Hermite setting (which we believe of independent interest). Indiana University Mathematics Journal ©.